Yes Arjuna has acted like a sarathi to Uttara Kumara in Mahabharatha on a special occasion. But Utterakumara was not even a king. Uttarakumara was the son of King Virata. King Virata has gone on a batttle with Thrigartha.
The padavas,after completing their 13 years of exile in forest, found safe disguised living in king Virat's palace. As per the conditions they are not be identified till they complete the full fourteenth the year in complete disguese. Sensing that the Pandavas were hiding in the Virata's Town, and that the King Virata has gone on battle, the Kauravas thought of attaking the Town and seizing the cows of the Virat Nagar. They new that the generous Pandavas should then come forward to protect the kingdom that sheltered them. It is on this occasion that the Uttara Kumara, the son of King Virat has boasted that he would have lead the battle, but he lacked a good sarathy to drive his chariot into battle. It was on this occasion that Arjuna ,who was in disguese by name Brihannala , came forward with the advice of Kanka (the name of Yudhistira in disguise) to assist during the emegency.
It appears you have mixed up some names and facts in the question.
In the great battle of Mahabharata, which was fought between Pandavas and Kauravas, Lord Krishna was Sarathi or Chariot driver of Arjuna.
Neither Arjuna nor Lord Krishna qualify to be called emperors. Arjuna was one of the five bothers, who formed the Pandavas side of the two warring groups in the war of Mahabharata. As Arjuna was not the eldest of the brother, he never became an independent king, let alone an emperor. Udhishthir,the Eldest of Pandavas brothers, was a king, but I am not sure if he ever adopted the title of emperor.
Krishna, a friend of Pandavas, and particularly Arjuna, was King of Dwaraka. To my knowledge, he made no attempts ever to expand his kingdom or to adopt the status of an emperor.